Having lost two matches in Group B previously, Merchant secured a crucial 4-0 win against Himanshu Jain to bag a spot in last eight.
Snooker and billiards professional Advani won his fourth straight round over Shahbaaz Khan to secure a quarterfinal berth.
Siddharth Parekh of Railways also came from behind to keep his hopes alive in Group C with a crucial win 4-1 over ONGC's Sourav Kothari.
Parekh's brilliant comeback sent Kothari crashing out of the competition and he will now battle world No. 26 Nigel Bond of Britain for the second spot in the group.
World No. 21 Stephen Lee of Britain and India's Kamal Chawla made it to the knock-out stage from Group A.
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